Name ______________________________________ Class ___ Simplifying Fractions Notes
Simplifying Fractions
1. Find a common factor for the numerator and denominator. (Pick a number that will go into
the top and bottom of the fraction evenly)
2. Divide both the top and bottom by the common factor
3. Keep dividing by common factors until you can’t do it anymore.
Ex.
12
÷2
----32
6
÷2
----÷2
16
3
3/8 is the simplified version of 12/32
------÷2
8
**WE ALWAYS SIMPLIFY FRACTIONS WHEN DOING ANYTHING!!!***
Simplifying (or reducing) fractions means to make the fraction as simple as possible. Why
say four-eighths (4/8) when you really mean half (1/2) ?
Simplifying Improper Fractions
An improper fraction is one in which the numerator is larger than the
denominator. If the answer to an addition, subtraction, multiplication, or
division fraction is improper, simplify it and reduce if possible.
Ex. 1:
4 is an improper fraction. Divide the denominator into numerator.
3
1
3 4 = 11
3
−3
1
Ex. 2:
10
is an improper fraction. Divide to simplify. Reduce.
8
1
2
1
10
= 8 10 = 1 = 1
8
8 4
−8
2
Ex. 3:
136
is an improper fraction. Divide to simplify. Reduce.
20
6
136 = 20 136 = 6 16 = 6 4
20
20
5
− 120
16
Simplifying Mixed Numbers
A mixed number is a whole number followed by a fraction. When simplifying
mixed numbers, remember to reduce the fraction portion of the mixed number.
When reducing the fraction, find a common factor that can be evenly divided
into both the numerator and denominator. Continue reducing the fraction until
there are no more common factors (remember, 1 does not count as a common
factor).
For example:
Practice:
Class 1 # 1-15
Simplify the following fractions. Reduce if possible.
Class 2 # 1-6
1)
6
=
5
2)
5
=
4
3)
7
=
3
4)
10
=
6
5)
4
=
2
6)
6
=
4
7)
15
=
3
8)
20
=
12
9)
19
=
4
10)
23
=
5
11)
18
=
3
12)
17
=
5
13)
37
=
9
14)
28
=
8
15)
47
=
9
16)
106
=
4
17)
17
=
2
18)
140
=
20
19)
162
=
10
20)
38
=
5
21)
52
=
3